• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.29-38
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• 2017

The main objective of this paper is to establish certain unified integral formula involving the product of the generalized Mittag-Leffler type function $E^{({\gamma}_j),(l_j)}_{({\rho}_j),{\lambda}}[z_1,{\ldots},z_r]$ and the Srivastava's polynomials $S^m_n[x]$. We also show how the main result here is general by demonstrating some interesting special cases.

• East Asian mathematical journal
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• v.31 no.1
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• pp.41-53
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• 2015

A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) ${\gamma}_k$ and the generalized Stieltjes constants ${\gamma}_k(a)$ have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants ${\gamma}_k(a)$ by choosing to use four known integral representations for the generalized zeta function ${\zeta}(s,a)$. As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants ${\gamma}_k$. Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.769-780
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. Very recently, Choi [6] presented explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function. In the present sequel to the investigation [6], we evaluate the log-sine and log-cosine integrals involved in more complicated integrands than those in [6], by also using the Beta function.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.321-333
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• 2011

During the last three decades, the problem of evaluation of the determinants of the Laplacians on Riemann manifolds has received considerable attention by many authors. The functional determinant for the n-dimensional sphere $S^n$ with the standard metric has been computed in several ways. Here we aim at computing the determinants of the Laplacians on $S^n$ (n = 8, 9) by mainly using ceratin known closed-form evaluations of series involving Zeta function.